Home MadLab Info Lambdaorder 
Lambdaorder 
Lambdaorder is a concept related to the lambdasearch algorithm. In my paper on this algorithm, you can find formal definitions and a lot more information, but to give you an idea of the concept, consider the following position: Black to capture 'a' Can black capture 'a? The answer is yes: White is captured in a simple ladder as follows: Ladder: lambdaorder n=1 Note that after each black move White is in atari (i.e. under a direct threat of being captured). After each white move, White is no longer in atari. After Black 5, White is doomed. In Go, this is called a ladder, and in the lambdasearch algorithm used in MadLab such a problem has lambdaorder n=1. This concept of threats and moving out of threats can be generalized. Consider the following position: Black to capture 'a' Now Black can no longer play an atari on the white stone. But he can still capture 'a'. This goes as follows: Loose ladder: lambdaorder n=2 Note that after each black move Black threatens to capture White in a ladder if White does not answer. After each white move, White can no longer be caught in a ladder. No matter what White plays after Black 5, White cannot avoid being caught in a subsequent ladder. In Go, such a problem is called a loose ladder, and in the lambdasearch terminology it is said to have lambdaorder n=2. This concept extends to other kinds of goals than capturing a single block of stones (e.g., doublegoal capture problems, connection problems etc.). Lambdaorders up to n=3 or n=4 ("loose loose ladders" and "loose loose loose ladders") are quite common in openspace tesuji problems, whereas problems with lambdaorder n=5 or more often have a somewhat different character (such problems typically have tsumego (life & death) or semeai flavour). So MadLab usually prefers problems with lambdaorder up to and including n=4, even though it can solve (some) problems of order 5 or higher. Enclosed problems can have very high lambdaorders. As an example the wellknown nakade shape has lambdaorder n=7. Black to capture "a" (lambdaorder n=7) This means that the attacker must spend n+1 = 8 extra moves on removing the white block (starting at Black "x"). This corresponds to White having 8 effective liberties as opposed to the 5 "physical" ones. MadLab does solve this problem. But if Black had had less liberties (7 or less to be precise), White would have had time to stage a counterattack on the black stones, and thus it would be a much more complicated (semeai) problem. Note that regarding singlegoals captures there is a relationship between the number of liberties of the block to capture and the lambdaorder: the lambdaorder to kill the stones is at least libs  1, where libs is the number of liberties of the block. So if a block has 5 liberties, it takes at least a lambdasearch of order 4 to kill it. So there is a correlation between lambdaorder and the number of liberties, but it is not a strict relationship. For instance, in the above figure White has 5 liberties, meaning that the problem could be solved in a search of lambdaorder n=4. However, the lambdaorder actually is as high as n=7. How do problems with lambdaorder n=3 look like? The following three problems are all of order n=3: Example 1 (n=3) As stated above, the concept of lambdaorder is not restricted to singlegoal capture tesuji's. The following gives an example of a doublethreat tesuji with lambdaorder n=2 (loose ladder): Example 2 (n=2, doublethreat)
